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What shape is the pool that you need to have cleaned and filled?

Ted remembers enough about geometry to know that he needs to determine the shape of the entire pool before he can determine its area. However, the shape of this pool does not fit any of the shape definitions he learned. The pool has straight sides, rounded ends, and no points. It doesn't seem to be a square, rectangle, parallelogram, triangle, or circle. Then, Ted recalls that although there is no name for this shape, it does have a classification in geometry.

Ted's pool is an "unknown" figure. An unknown figure, in geometry, is any shape that does not fit a specific geometric definition. Look closely at the examples of known and unknown shapes shown below.

Known Figures

Unknown Figures

rectangles and squares triangles circles
Rectangles and
Squares
Triangles Circles

What makes these figures "known"?

All of these figures have specific labels and definitions in geometry. There are established formulas for calculating the area of each figure.

swimming pool paint palette house
Swimming Pool Artist's Palette House

What makes these figures "unknown"?

These figures don't fit into a specific geometric definition, although they all have characteristics in common with "known" figures. There are not established formulas for determining the area of shapes like these.